A148417 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 1), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 18, 53, 195, 679, 2644, 9717, 39573, 152777, 634106, 2534293, 10725654, 43864275, 188331104, 785364407, 3407302997, 14424526791, 63162786264, 270620636929, 1193897835004, 5167714383915, 22940303142910, 100140177907925, 446966463581657, 1965207313524605, 8812497687855266

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A056296 A293964 A275079 * A148418 A148419 A148420

Adjacent sequences: A148414 A148415 A148416 * A148418 A148419 A148420

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved